Massachusetts' public colleges and universities excel at attracting students but trail those of other states in graduation rates, a new state study has found.

On Thursday, the state Department of Higher Education released its first comprehensive look at where the 29 state schools stand in comparison to their counterparts across the country, and introduced goals for public higher education in Massachusetts.

"It gives us a sense of where some of our effort needs to be placed," Cape Cod Community College President John L. Cox said.

The study is part of the state's "Vision Project" for higher education that began in 2010.

The study found that the state's 15 community colleges, nine state universities and five University of Massachusetts locations enroll about 77 percent of recent high school graduates, as compared to the 65 percent national average.

But the state lags behind in both six-year and three-year graduation rates, and pass rates on national licensure exams.

And high school students in Massachusetts are also not as prepared to enter college as are students in other states, according to the study.

Cape Cod Community College in West Barnstable and Massachusetts Maritime Academy in Bourne have programs in place to try to close that gap.

The community college, for example, uses its College Connection program to reach high school students before graduation, and hopes to soon offer classes at high school campuses, Cox said.

At MMA, which includes a regimented lifestyle and a focus on STEM subjects — science, technology, engineering and math — graduation and licensure passing rates are higher than the state average. But that doesn't mean the school couldn't do even more, president Adm. Richard Gurnon said.

"We think Massachusetts ought to be No. 1 in public higher education ... so I welcome the scrutiny that the Vision Project calls for," he said.

Gurnon was head of the state university presidents' group when the Vision Project began, Katy Abel, spokeswoman for the Department of Higher Education, said.

The state's main challenge in increasing graduation numbers is a lack of funding, both Cape college presidents said.

According to the study, Massachusetts "ranks 30th among states in higher education funding per student."

"The quality of the instruction needed demands high salaries. The quality of the research demands laboratory equipment. Simulations in high-tech fields, all that comes at a significant cost," Gurnon said.

Both of the Cape's state colleges were lauded in the study for their programs that aim to reach out to high school students, young women and K-12 teachers.